Solve for $x$ and $y$ using elimination. $\begin{align*}3x+y &= 8 \\ -2x-y &= -9\end{align*}$
Solution: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $x = -1$ $x = -1$ Substitute $-1$ for $x$ in the top equation. $3( -1)+y = 8$ $-3+y = 8$ $y = 11$ $y = 11$ The solution is $\enspace x = -1, \enspace y = 11$.